Flux Line Channels and Reduced Hall Effect in Impure 2D Superconductors
We have studied the dynamics of flux-lines in an impure two-dimensional superconductor using numerical Brownian dynamics. In the dirty pinning limit and for small center-of-mass velocities the flux lines prefer traveling in narrow channels uniquely determined by the pinning configuration. At a certain critical drag force there is a dynamic transition from this glassy state into a more ordered crystalline state, in which the channel structure vanishes. The channels are studied by monitoring the particle trajectories and the spatial distribution of vortices. By explicitly including a Magnus force in the Langevin equations of motion we induce a Hall field and we find that the effective Hall angle is strongly reduced by the formation of channels, i.e. the channels introduce a transverse energy barrier that guides the motion, predominantly in a direction parallel to the external force. The transverse depinning force is larger than the depinning force in the direction of the drag and thus the Hall field actually vanishes at finite velocities. We propose that the Hall angle can serve as an order parameter for experimental detection of the glass to crystal transition. Our results are in excellent agreement with recent predictions made by Giamarchi and Le Doussal (cond-mat/9512006).